Preheat the oven to 375 degrees F (190 degrees C).
Spread oil in a 9x13 inch baking dish.
In a large bowl, mix together the apples, pomegranate seeds, brown sugar, and nutmeg.
Spread evenly into the prepared pan.
In the same bowl, stir together flour and sugar.
Mix in oil until the mixture resembles crumbs.
Sprinkle over the top of the fruit.
Bake for 45 minutes in the preheated oven, until the apples are soft.
Let stand 10 minutes before serving.
Serve warm or at room temperature.